Gerunds and infinitives are often interchangeable, both as subjects and objects of verbs. Compare:

Smoking is injurious to health.
To smoke is injurious to health.

Playing games is good for health.
To play games is good for health.

We began to talk about old times.

We began talking about old times.

I intend to visit them next week.
I intend visiting them next week.

However, in some cases there is a difference of meaning.

Study the following sentences.

James likes singing.
He would like to sing a devotional song on this occasion.

Here the first sentence means that James likes singing as a form of art. It is a general statement. The second sentence means that James likes to sing a particular song on a particular occasion.

He likes playing tennis.
He would like to play tennis this evening.

The first sentence is a general statement about his liking for tennis as a game. The second sentence is a statement about playing tennis on a particular occasion.

Thus we can see that the gerund is used for making general statements and the infinitive for making statements about particular occasions.

After some verbs we can use an –ing form, but not normally an infinitive.
Examples are: enjoy, finish, give up, suggest etc

The doctor suggested taking a long holiday. (NOT The doctor suggested to take a long holiday.)
I enjoy traveling. (NOT I enjoy to traveling.)