A definition you can use
Artificial intelligence is the business of getting computers to do things that, when a person
does them, we call intelligent: recognising a face, understanding a request, planning a route,
writing a summary, deciding which of two options is better.
That definition is deliberately about behaviour. It says nothing about consciousness,
understanding or feeling, because nobody can measure those in a machine, and the argument about
whether they matter has run for seventy years without settling. What you can measure is whether
the output is any good.
Three words people use interchangeably, wrongly
Artificial intelligence is the whole field, including approaches that do not
learn at all. A chess program from 1985 that follows hand-written rules is AI.
Machine learning is the part of the field where the system improves by
processing examples rather than by having rules written for it. Nearly everything built since
2012 is machine learning.
Deep learning is machine learning done with neural networks of many layers. It
is a subset of a subset, and it is what people usually mean when they say "AI" today.
The rule of thumb
If someone wrote down the conditions, it is a program. If the conditions were inferred from
data, it is machine learning. The difference matters because you can read a program and argue
with it, and you mostly cannot do that with a model.