たく is a verb suffix and it's also a modified form of たい. The たい suffix indicates desire and is attached to the end of verbs.
In this example, we have the verb 泳ぐ, which is the infinitive form (often referred to as the dictionary form).
To turn 泳ぐ into the たい-form, you simply change the verb stem to 泳ぎ and add たい to the end. All verbs to this. For example:
する > し > したい = want to do
書く > 書き > 書きたい = want to write
行く > 行き > 行きたい = want to go
Does this all make sense? If you need further examples or help conjugating verbs, let me know.
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I should have also added that たい will become たく if the verb is negated. So, the resultant ending will be:
~たくない・たくありません