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This isn't explained on the spellcasting section of the warlock.
On the table, it's shown the warlock acquires new spell slots as it levels up, for example, starts at level 1 with 1 1st level slot, and then on level 2 it gets 2 1st level slots; however at level 3 it says it still has 2 slots, but now are 2nd level. Does this means he gets 2 2nd level slots? Or the 1st level slots are lost and he has very limited slot uses of 2nd level?
All warlock spell slots are the same level (PHB p.107, under the Spell Slots section). As they gain warlock levels, warlocks eventually reach their maximum of 4 spell slots (at the 17th level of warlock), and their maximum spell slot level of 5 (at the 9th level of warlock).
Do note that you can cast spells with slots that are higher level than the base spell. For example: hold person, a second level spell, can be cast with any spell slot of level 2 or higher. If you were to cast it with a higher level slot, it would even count as a spell of that higher level. Many spells even specify additional effects when you cast them at higher level, though not all do, and they don't need to have such a feature in order to be able to use a higher level slot.
In addition, the reason for the relatively limited number of slots is that warlocks regain their spell slots on a short rest as well as a long rest (unlike most other spellcasting classes).
