A verb is a grammatical class of word. They are sometimes called 'doing words' though this does not really fit all verbs.
Verbs have different forms. There is the infinitive form, which is the verb in its basic state. For example - 'run'. This is sometimes called the 'bare/base infinitive' or the 'infinitive without to'.
Another form of the infinitive is the 'full infinitive' or the 'infinitive with to'. For example 'to run'.
Verbs can be made into nouns by adding 'ing'. These types of nouns are called gerunds. For example in the sentence "I like running" the word "running" is a gerund.
Verbs also have another form which looks identical to the gerund which is called the present participle form. For example in the sentence "He was running around the track when a dog tripped him up" the word "running" is the present participle form of the verb 'to run'.
The past form of a verb is used in the tense the past simple. For example in the sentence "I ran down the street but still missed the bus" the word "ran" is the past form of the verb 'to run'.
The past participle form of a verb is used to make different verb structures such as the present perfect. For example, in the sentence "I've run every day since I was 23" the word "run" is the past participle form of the verb 'to run'.
Tenses are grammatical structures using verbs. English has only two tenses, the present simple and the past simple. However English does have other forms which use verbs. For example the perfect and continuous forms. These are not actually tenses though they are often described as such.