Linear search, also called sequential search, is the most basic way to look for a value in a collection: start at the beginning and examine each element in turn until the target is found or the end is reached. It needs no special preparation of the data and works on any list, sorted or not. In the worst case, when the target is at the end or not present at all, it inspects every element, so its running time is O(n) in the size of the collection.
Because it makes no assumptions about ordering, linear search is the right choice when the data has no exploitable structure. If a list is unsorted and not indexed, there is no way to rule out elements without looking at them, so checking each one is unavoidable. This makes linear search optimal precisely in the cases where faster methods like binary search cannot apply.
Donald Knuth discusses sequential searching as one of the core methods in Chapter 6 of Volume 3 of The Art of Computer Programming, alongside searching by comparison of keys and by hashing. It serves as the baseline against which more elaborate search strategies are measured.
The contrast with binary search is instructive. Binary search is far faster but requires sorted data; linear search is slower but requires nothing. The MIT 6.006 lecture notes describe this in terms of the comparison model: a sorted array supports logarithmic search, while an arbitrary unordered array forces a scan that is linear in the number of items.