Bit more of a long winded and simple illustrative examples.
Your Pokemon don't have visible levels. They have a CP number. Basically this is the current value of all their stats in a "Combat Power" rating. (They do effectively have a level behind the scenes I'll come on to that).
The half circle bar shows their CP value and progress to maximum CP value (This maximum CP is based by on current level - again will come onto that).
Each Pokemon is different and CP values/max CP value will vary for each capture. One Weedle might be 4/25 and look much weaker with a barely complete bar, but it's actually better than the 7/8 one who's bar is nearly full - as it can grow stronger.
(A species will be capped at certain values though. That's why we're talking about specific Pokemon and IVs above. e.g. A Weedle at this level will have a potential max CP of 30 at this level [so the 25 one is pretty close to perfect] but a Dragonite will have a potential max CP of 50 at this level)
Every time you capture a Pokemon you get 3 Candies for it's species (or more if you capturing an evolved version. e.g. a Pidgey will give you 3, and Pidgeotto will give you 5)
You "power up" Pokemon by spending Candy and Stardust. (You get Stardust from capturing Pokemon. It is RARE AS SIN later when power ups can take 4000. Only use when you really want to).
So you can power up that 4/25 Weedle to 6/25, 8/25 etc all the way to 25/25 - but should you?
So Pokemon Level. It's effectively based on your trainer level. So at your current level that Weedle can go up to 25. If you level up it can now go up to ,say, 35. (It'll go from 4/25 to 4/35, or for instance 25/25 to 25/35).
But Weedles you capture will now be "up to 35" so you have a better chance of catching higher CP Pokemon as your trainer rank levels up. So it's probably not worth Powering up those Pokemon you catch now - because you'll easily get more powerful Pokemon when you level up trainer ranks. (i.e. you spent all your Stardust to make what's now a 25/35 and then you capture a 26/35 one!)
That's a very simple basic of why I'm saying to catch more - it's the quick simple way to get your Trainer level up, and most of the Pokemon you capture now (even if amazing) are likely to be quickly beaten.
Getting your trainer level up is the early priority.
(That's also why I'm saying hold off on Evolving, which takes Candy, but not Stardust. Evolving, especially when making new discoveries, is an excellent source of XP. Save it until you can blow a Lucky Egg (which doubles XP gains) and do lots. E.g. My last egg I evolved 35 Pidgeys. Should be 17.5k xp, egg made it 35k