I saw a boy mending his shoes. Here ‘mending’ is a/an -

Participle is a non-finite verb. It is used as an adjective. 
There are three types of participle:
a. Present Participle: When ‘verb+ing’ works as an ‘adjective and verb’, it is called Present
Participle.
Example: Standing at the door, he knocks.

b. Past Participle: When ‘v3’ works as ‘non-finite verb’, it is called past participle.
Example: The burnt house is not ours.

c. Perfect Participle: When ‘having’ is used as ‘adjective and verb is called perfect participle.
Example: Having done the work, I slept.

Functions:
1. It takes an object like a verb:
Hearing a noise, he woke up.
I saw a boy mending his shoes.
The participle took objects (‘a noise’, ‘his shoes’) like a verb.