As you are aware, the tags you mentioned are all struts tags.
The tag <logic:present ..> is similar to the normal 'if' loop of java.
if property named lastname exists then enter the loop and do the rest.
similarly <logic:equal ...> ,meaning if the value of the property named 'age' is equal to value 'a' then do this or else do the rest.
and the struts tag <bean:write..> is used to display the output of the
form property value on the screen.
For more clear understanding ,better you go thru the struts HTML,LOGIC,BEAN tags and its libraries.