Hello. This is a long answer, but I hope to provide you with comprehensive, useful information.
Here are what the numbers in your summary mean, and also some information and thoughts on the affects of those numbers:
The white stat in your pokemon's summary is called its "base" stat, I'm sure you already have some understanding of this, such as pikachu(90 base speed) being a faster pokemon than geodude(20 base speed.) Or Umbreon being more defensive than an Espeon. The base stat of a pokemon determines the rate at which that stat will grow and what limit it reaches at level 100. However, that limit can be affected and increased with IV's, EV's, and Nature.
The orange stat is the Individual Value, or IV. This is a randomly assigned number upon catching a pokemon. The IV's can range from 1-31, and they have their full effect on the base(white) stats at level 100. Meaning if you have 31 IV points in the Attack stat, at level 100 you will have an "extra" 31 points added to your Attack stat. This is why high IV pokemon are generally most desirable. But say, for a pokemon like alakazam, you won't be worried if it has a low Attack IV since it doesn't use physical attacks. Furthermore, these stats are more important for the competitive aspect of battling. While this is only my opinion, 1-31 points aren't such a big deal in normal gameplay. In competition, where just 1 HP or 5 more attack or defense points could determine the winner in a battle, good IVs become most important for your pokemon. IV's also determine the type the move Hidden Power will be if you happen to learn that move.
The Nature of a pokemon is seen in your summary, such as adamant or timid. Nature effects a stat's growth(not including HP) by 10%, and lowers another's growth by 10%, depending on the nature. Fortunately for this game, you can see the effect of certain natures in your summary - the Booster Stat is highlighted Green, the Hindered Stat is highlighted Orange. As you can surmise yourself, you don't want your Alakazam to have an adamant(I think) nature which boosts its attack and lowers its special attack, but rather a modest nature or one which increases speed. Natures are more important to normal gameplay than IV's are, as their effect is immediate to the stats of a pokemon. Meaning, once you catch an adamant Magikarp, its attack stat is already boosted 10% of the base growth. I'm sure you can see why people are so picky with the stats of a pokemon, as the IV's and Nature are qualities of a catch which cannot be change or be altered.
Now, EV's, or Effort values, are stats which can be altered. Your Effort Values are the Blue stat you can observe in your pokemon's summary. An Effort Value is a stat which may be earned upon fainting a pokemon, a pokemon may give 1 to 3 effort value points of a certain stat among two stats. To put it another way, a pokemon like Rattata will give you 1 speed EV upon fainting it, but a Beedrill will give you 2 attack EV's and 1 SP.Def EV. To observe which pokemon gives which EV's, lay thine eyes upon this excellent resource - EV Output by Pokemon
Here is how EV's effect your pokemon's base(white) stat. Upon earning 4 EV points of any stat, your pokemon will gain 1 real stat point of the respective stat. Meaning, once you earn 4 Attack EV's, your white stat which was hypothetically 20, is now 21. In this way, you can tailor your pokemon's stat growth to your desire, such as raise a Magikarp or Gyarados with the stats EV trained in Attack and Speed. Furthermore, it takes 252 EV points before the EV limit for a particular stat is reached. You may earn up to 510 EVs. This means that you may invest 252 in two stats, and have 6 left over for **** and giggles. However, if you so choose, you may distribute the stats in any other fashion such as allocating 252 points to HP, 124 to DEF, and 124 to SP DEF, or whatever idea you have for whatever purpose. The most commonly done thing though is to just max out two stats and be done with it. This is to gain the most possible stats of a pokemon for it's effective purpose. I find that sometimes distributing the points to more than two stats to be more beneficial.
In PRO, EV training is more time consuming than it is in the newer games. However, you may obtain an item called Macho Brace in Goldenrod City, Johto, from a trade with a biker in front of the Pokemon Center. By having your pokemon hold this item, it will cut your pokemon's speed in battle by 50%, but it will Double the amount of EV's you gain in battle. So instead of getting 1 speed EV from a Zubat, you will now gain 2. Fearow will naturally give you 2 Speed EV's, so with the Macho Brace it will become 4. This allows for faster EV growth. Please lay thine eyes upon this topic to register in your head space the best locations to EV train certain stats - EV Training Hotspots
The last thing about EV's: you may reduce your EV's by using EV reduction berries which are sold by players, or are obtainable from the Berry Tower. You may also raise your EV's by using training medicine like Protein and Calcium, which will give you 10 EV's for their respective stat. The use of these medicine items is limited to 10 uses, or 100 EV's per stat boosting item.
Please refer to Bulbapedia to observe the base stats of a pokemon by utilizing the search function. Other good sources are, Serebii and Smogon
My personal favorite is Smogon, as the information page on the pokemon is most easy on the eyes, the base stats are clearly visible, and you can see suggestions for EV spreads, and also potentially useful movesets. However, the learned moves in PRO as well as their availability might differ a little bit from all of these sites. To know which moves your pokemon will learn and when, click on your in-game pokedex, search the pokemon with the search bar, and lay your eyes upon the glorious information which it provides.
To understand the usefulness of base stats and abilities, think about the things a pokemon does in battle and what will help it achieve those things. Think about an Alakazam. It has a measly 45 Defense base. Surely you don't plan to use it as as physically defensive pokemon. Neither would you use it as a physically offensive pokemon, as its base attack is just 50. However, it's base SP.Atk is 135 and it's base Speed is 120. It is clear this is a pokemon you want to outspeed your enemy with, and to faint with as few moves as possible. Contrary to this, a Gyarados has stats which favor it's use as a physically offensive pokemon, but it also has some bulk. Thinking more about this and bringing in abilities, the most useful abilities Gyarados can have are Moxie, and Intimidate. Depending on how you use Gyarados, Intimidate may be useful to switch in and lower the enemies attack with, it's not a bad pokemon to switch into an attack that isn't super effective because it's somewhat bulky and in this way Intimidate may be useful. But Moxie will raise your attack by one stage upon each faint your Gyarados achieves. If you wish to kill as much as you can with your Gyarados, Moxie will be most useful, if you wish to annoy and bother enemies with stat reduction or perhaps get them to switch out, Intimidate may be more useful.
I hope this has helped you and answered your question and perhaps more. You don't need to memorize every ability's function or base stats if you utilize the recourses online. But with time and experience, you will naturally retain such information. You may not memorize exactly what the base stats of a pokemon are, but you will have a general idea of a pokemon's usefulness and potential based on it's best stats and most useful abilities for the purpose that pokemon serves.
