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Tablature ("tabs") Explained
Traditional notation shows the notes.
Tablature shows the fret numbers for each string. You don't have to know the notes.
This song starts with 0 (no strings fretted) then fret 2, fret 4, fret 2, and so on using the fret numbers to navigate.  In this example, only the first string (farthest from your chin) is used. A "0" means that the string is sounded but no fret is pressed.
Although tabs don't show how long to hold each note, they make it easy to play familiar songs.
Tabs are especially helpful in writing out arrangements that use all three strings.  
The three strings are represented left to right, with the bass string at the bottom. 
Numbers aligned in a column are sounded together.  Here, some simple harmonies are used.
Some simple chords are used in this example.
In all three examples, the melody is played on the top string.  This is so typical of dulcimer playing that the top string is often called the "melody string".
Advanced technique:
Sometimes it's more convenient to distribute the melody across the strings.  Playing this way lowers the pitch and minimizes hand travel. 
Here's a whole song written out in tablature.