There are two main aspects which make an algorithm better than another. The first one I would like to discuss is the measure of how efficient an algorithm is in terms of the time the algorithm takes to complete its calculations and come to a result (an end).
Consider the examples as outlined by Brookshear (2009) of a binary search and a sequential search for a specific item in an ordered list. While the sequential search runs through a list one by one until it finds an entry, on average this search will search through at least half of the list – if the list is very large this may add up to quite a sufficient amount of time per search. A binary search divides a list into two, looks at the middle entry and calculates whether the result is in the first or last half of the resultant lists, then further breaks the respective half in half again, and repeats this process until it finds the item it is looking for. One can plainly see that the binary search method will access a record far less times on average than the sequential search.
Another aspect of measurement is the physical space the algorithm consumes when performing its calculations/operations. A very simple way of explaining this is the one of sorting a list alphabetically. The two methods are firstly the bubble sort versus secondly creating a new list in the correct order. In the bubble sort the method is to sort the list in the form of looking at it in small pieces and sorting them by shuffling around the entries until the entire list is sorted. This way we only occupy the memory/space of the original list. In the method of sorting into a new list, the memory occupied by the original list is used and another entire list is created from the same entries sorted into the correct order. The latter occupies double the amount of memory than the former.
References
Brookshear, J.G (2009) Computer Science: An Overview. 10th ed. China: Pearson Education Asia Ltd.