1

犬は泳ぐことが出来ます。

A translation for this sentence would be 'The dog can swim', right? Is it necessary to use ことが? And what does it mean?

3

こと here is a nominalizer, and it's necessary because ~ができる only takes a noun. See this question, too. Literally, 泳ぐことができる is translated as "can do swimming" rather than "can swim".

泳ぐことができる and 泳げる both basically mean "can swim". But as you can easily guess, the longer version is more explicit about the ability, and sounds a bit more formal/technical. The former sounds closer to "have an ability to swim" rather than simple "can swim."

0

The following is pretty clear & concise :

http://study.u-biq.org/33.html

  ・[noun] が できます。     ---     example:   スキーが できます

  ・[verb (dictionary-form)] ことが できます。

                ---     example:      およぐ こと が できます。

                               Oyogu koto ga dekimasu

There probably are other good pages.

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