~mashou” means “Let’s do something”. For example : Let’s play (Asobimashou). It is as simple as ABC ;)

Examples
Kobayashi : Today, where do you go? - Kyou, doko e (iku)ikimasu ka?
Tony : I will be going to Shinjuku - Shinjuku e ikimasu
Kobayashi : How about you? - Anata wa?
Michael : I will be going to Shinjuku too - Watashi mo Shinjuku e ikimasu
Tony : Then, let’s go together - Jaa, issho ni ikimashou ka?
Michael : Alright, let’s go - Ee, ikimashou
Meaning : Kyou (Today), Doko (Where), Issho ni (Together)

Other Examples
Let’s drink coffee at the coffee shop - Kissaten de ko-hi- o (nomu)nomimashou
Let’s erase off the words on the blackboard - Kokuban no ji o (kesu)keshimashou
Let’s sing Japanese songs - Nihongo no uta o (utau)utaimashou
Meaning : Kissaten (Coffee Shop), Kokuban (Blackboard), Ji (Words), Kesu (Erase), Uta (Songs), Utau (Sing)

aAAAAAAAAAA