There are many variations of the shield: this description is taken from information presented by the Historical Research Center Inc. In heraldic terms, the "blazon of arms" is - Barry of six or and azure on a canton argent three roses gules placed two and one. In other words, the shield has six horizontal bars, gold and blue, with three red roses on a silver area at top left, placed two above one.
Gold denotes generosity, blue loyalty & truth, silver purity & innocence. Red roses, first among flowers, denote beauty and grace.
The variations mainly concern the area to top left, with different heraldic devices being placed there. The most common one is a "chaplet", or circular garland, of roses or leaves rather than the three individual flowers.
There are two mottos associated with the arms. The one given by the Historical Research Center Inc. is Holme semper viret, which may be translated as "Holme is always green". This almost certainly refers to the Holm Oak (Quercus Ilex), an evergreen tree bearing acorns but with leaves more reminiscent of holly or bay. The other is Fide Sed Cui Vide, meaning "Trust, but be careful of whom you trust" - wise words indeed!
"Holm" is a Scandinavian word meaning "small island", so the surname Holmes may well have a Nordic root, either by direct ancestry or given to those living in an area inhabited by Scandinavians, possibly during early medieval times.