This is basic organic chemistry. CIS vs. TRANS. Were you not taught this?
If you have a double bond between carbons, you cannot rotate around this bond. With single bonds you can so if you had Cl-CH2-CH2-Cl for instance it doesn't matter where the Cl atoms are located on the carbons because the single bond can do a full rotation.
However if you have something like CH3-CH=CH-CH3, the double bond prevents the CH3-CH on either side from rotating fully around. So each carbon in the middle has an H and a CH3 group attached to it. Picture one on the top and one on the bottom. Now consider the other side of the double bond. Put either the CH3 or H on top and the other on the bottom. Now look across the double bond. If both H atoms are on top or if both are on bottom, you have a CIS double bond. If one H atom is on top and the other on bottom, you have a TRANS double bond.
So in monounsaturated fats, there is (by definition) one double bond. Fatty acids consist of a hydrocarbon chain. If there is a double bond there, it can't rotate around the double bond. There should always be an H atom on each carbon of the double bond. If both of these H atoms are on the top or the bottom, it is CIS. If one is on the top and one on the bottom, it is TRANS.
The body likes to have CIS. The CIS version puts a kink in the molecule (picture the letter 'V' where the double bond is on the bottom of the letter). The TRANS version keeps the hydrocarbon chain more or less linear, causing them to stack on themselves better and making them more likely to stick together. That's why trans-fatty acids are unhealthy.