reisen
to travel
To move over a longer distance from one place to another, often for pleasure, for business reasons, or to discover something.
Nächstes Jahr wollen wir durch Südostasien reisen.
Next year we want to travel through Southeast Asia.

to travel
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to travel
To move over a longer distance from one place to another, often for pleasure, for business reasons, or to discover something.
Nächstes Jahr wollen wir durch Südostasien reisen.
Next year we want to travel through Southeast Asia.

'Reisen' (to travel) is a verb of movement and always forms the perfect tense with the auxiliary verb 'sein' (to be). So it is 'ich bin gereist' (I traveled / have traveled), not 'ich habe gereist'.
Letzten Sommer sind wir nach Italien gereist.
Last summer we traveled to Italy.
The verb 'reisen' (to travel) belongs to the word family around 'die Reise' (the trip/journey). If you know one word, you can understand and use the other more easily.
Unsere Reise durch die Berge war unvergesslich.
Our trip through the mountains was unforgettable.
The preposition after 'reisen' (to travel) depends on the destination. You travel 'nach' cities and most countries, 'in' countries with an article (e.g., in die Schweiz), and 'durch' regions or areas.
Nächstes Jahr reise ich nach Spanien.
Next year I am traveling to Spain.
'Reisen' (to travel) is often combined with adverbs that describe the purpose or type of trip. Common examples are 'geschäftlich reisen' (to travel for business), 'privat reisen' (to travel privately), 'allein reisen' (to travel alone), or 'mit der Familie reisen' (to travel with the family).
Mein Chef reist sehr oft geschäftlich.
My boss travels for business very often.
to stay / remain
'bleiben' and 'reisen' are clear opposites here. 'bleiben' means that you stay in a place and do not leave. 'reisen' means that you move to another place, often over a longer distance. If someone stays at home, they are not traveling at that moment. If someone travels, they leave the place where they were for a while.

Im Sommer reisen wir mit dem Zug nach Italien.
In the summer, we're traveling to Italy by train.
Wegen des schlechten Wetters bleiben wir heute zu Hause.
Because of the bad weather, we're staying at home today.