Transitive:

The word transitive comes from the Latin transire meaning ‘to pass’, ‘to cross’, ‘to go beyond’, therefore it describes actions that move from the subject or doer directly to the object, without making use of prepositions such as di, da, per, a etc.
Examples:
The classic example that we learn at school is: io mangio la mela (I eat the apple); in this sentence io is the subject of the verb, mangio is the transitive verb, and la mela is the direct object.
It’s not always necessary to express the direct object, for example: la sera mangio presto (in the evening I eat early). Here, the direct object would be ‘dinner’, ‘meal’, or ‘food’, but it is implicit rather than expressed.
Another example would be: Giovanni guida la macchina per andare a lavorare (Giovanni drives his car to go to work). Here, guidare is a transitive verb because it is followed by the direct object, la macchina. However I could also omit ‘la macchina’ and simply say Giovanni guida per andare a lavorare.

Intransitive:
When using intransitive verbs, the action does not move directly from the subject to the object but makes use of a preposition such as di, da, in, a etc.
Some important intransitive verbs are those which don’t express an action but rather a state or a condition, such as essere (to be), stare (to stay), divenire (to become), or movement such as andare (to go), venire (to come), arrivare (to arrive), etc. When using these verbs we frequently add information, such as ‘where’, ‘when’, ‘how’, ‘for how long’, and so on.
Examples:
il treno è arrivato in stazione (the train arrived at the station). Here, il treno is the subject, è arrivato is the intransitive verb, in stazione is the indirect object introduced by the preposition in
sto in ufficio tutto il pomeriggio (I’ll be in the office all afternoon)
Giovanni va al lavoro in macchina (Giovanni goes to work by car)