The name is Danish. "Steen" is a first name (male). "gaard" is the old spelling of the word "gård", which is the Danish word for "farm". The word can be used to describe anything from a one-room homestead to a large manor house or estate. "Steensgaard" thus denotes a farm owned or named after "Steen". When people became required by law (in Denmark) to have a last name, many chose the name of the farm they were affiliated with. The law was enacted in 1828, but was not uniformly enforced until about 40 years later.
An alternative spelling of the above-mentioned first name is "Sten", which incidentally also is the Danish word for "rock" or "stone". The name "Steensgaard" is therefore sometimes jokingly "translated" to "Stonyfarm".
The Danish spelling reform of 1948 introduced the letter 'å' to replace 'aa' (which was and is considered a single letter in Danish). However, for proper names the change was optional. Many people chose to remove the second 'e' at the same time. Hence, the following names are common variations: Steensgård, Stensgaard, Stensgård.