Usage

As adjectives, participles can modify nouns.

I see the man swimming
which in Latin would be:
video hominem natantem

They can also be used to make more complicated sentences.

I see the man who is carrying the amphora
which can also be expressed as:
I see the man carrying the amphora
which in Latin would be:
video hominem amphoram portantem

They can even replace a noun entirely,

I see the person swimming
which in Latin would be:
video natantem

With perfect passive participles and future active participles you can also tell the gender of the word, and thus supply a missing noun as necessary.