Answer & Explanation:
(I have included some audio examples of each at the bottom).
Staccato:
Here is the definition of Staccato:
Staccato is a form of musical articulation. In modern notation, it signifies a note of shortened duration, separated from the note that may follow by silence.
My shortened simpler explanation: Staccato is a short note that could also be decried as 'Sharp' or 'Sudden' (in a way). Some could say its like a sudden attack on the piano keys or a sudden strike on the guitar strings, ect.
Legato:
Here is the definition of Legato:
Notes played in a smooth flowing manner, without breaks between notes.
I would do my own definition for legato but the definition above is as accurate as it could be.
marcato:
Here is the definition of marcato:
is a musical instruction indicating a note, chord, or passage is to be played louder or more forcefully than the surrounding music.
My Shortened and simpler explanation:
When you play a song, if you see the marcato symbol (Wich is just this, ^, above a note or a chord) it simply just means, make that note or chord louder than the rest of the notes or chords around that. Its like an accent. If there was 3 people that had a stereotypical British accent and one person had an irish accent then it would be a tiny bit like the person with the irish accent was just speaking in marcato. Except marcato means to play a note louder or make it stand out to the rest of the notes and chords.
So in conclusion, the difference between Staccato, legato and marcato, is that staccato is a short and 'sharp' note, legato is a smooth and flowing note without breaks in between, and marcato, is a note that is louder and more noticeable and sticks out from the rest of the notes and chords.
I really hope my answer helped as it took me along time to type!! :)