What does specific or highly specific in nature means ?

Lets take a example of enzymes. These are highly specific in nature thereby meaning that they cannot catalyse every reaction and perform a function for a particular reaction only. 
For eg. -  Urease is a enzyme which catalyses the hydrolysis of urea only (NH₂CONH₂). It does not catalyse hydrolysis of any other amide ( RCONH₂).  Thus, we can say that, urease is specific for the hydrolysis of urea, that is, it is used to perform that particular task only.

${\mathrm{NH}}_2{\mathrm{CONH}}_2 \stackrel{\mathrm{urease}}{\to } 2{\mathrm{NH}}_3 + {\mathrm{CO}}_2$

$\mathrm{RCONH}2 \stackrel{\mathrm{urease} }{\to } \mathrm{no} \mathrm{reaction}$