Fertilizers are compounds that contain elements which are essential as plant nutrients. The primary plant nutrients are nitrogen, potassium and phosphorus. These have to be supplied separately as plants cannot use nitrogen directly from the atmosphere and soil is usually deficient in potassium and phosphorus. A particular fertilizer could have compounds of one of these elements or can be a mixture of compounds containing all the nutrients. The rate of growth of plants increases with the use of fertilizers and they are more healthy. For the lawn of a golf course this would ensure the grass is green and can withstand movement on it.
Herbicides are chemicals used to kill plants other than those being grown. The presence of other plants decreases the nutrients available to the plants being cultivated and in the case of the lawn would spoil the appearance.
Therefore in a golf course both fertilizers and herbicides are used to maintain the lawn.