A cross-spectrum herbicide is a selective herbicide that kills or controls both groups of weeds: broadleaf and grasses. Cross-spectrum is also known as broad-spectrum. However, broad-spectrum term might be confusing since, as said above, this type of herbicide kills/controls grasses on top of the broadleaf ones.
So cross-spectrum is a synonim for broad-spectrum.
Now, I defined what a cross-spectrum herbicide is, this type of herbicide must be put in context.
When talking about herbicides you might have heard about different herbicide attributes like: total, broadleaf, grass, selective, non-selective, cross-spectrum, etc.
Total herbicides are the ones that kill everything, the weeds and the crops. They are also called non-selective.
Selective herbicides are the ones that kill the weeds but not the crops (in some cases they still damage the crops). Within the selective herbicides we have, broadleaf herbicides which only kill broadleaf weeds (so they do not kill all the grass weeds); grass herbicides which only kill grass weeds and lastly we have cross-spectrum herbicides which kill both broadleaf and grass weeds.

All these can be summarized on this table. We also added a column called crop in order to show that some GMO-crops are resistant to some total herbicides.
Note: All this information has been gathered from homologa.com team
Crop | Herbicide | Effect on grass weeds | Effect on broadleaf weeds | Effect on the crop (if applied all over) |
Non-GMO Cereal | Broadleaf | None | Kill | None |
Non-GMO Cereal | Grass | Kill | None | None or very limited |
Non-GMO Cereal | Cross-spectrum | Kill | Kill | None or very limited |
Non-GMO Cereal | Total | Kill | Kill | Kill |
GMO-cereal | Total | Kill | Kill | None |