Didst send a plentiful rain - נדבות גשם geshem nedaboth, a shower of liberality. I believe this to refer to the manna by which God refreshed and preserved alive the weary and hungry Israelites.
Thou, O God, didst send a plentiful rain - Margin, shake out. Prof. Alexander, “a rain of free gifts.” The Septuagint and the Vulgate render it, “a voluntary or willing rain.” The Syriac, “the rain of a vow.” The Hebrew word translated “plentiful” means free, voluntary, of its own accord - נדבה nedâbâh - (See the notes at Psalm 51:12, where it is rendered free); then it means that which is given freely; and hence, abundantly. It means, therefore, in this place, plentiful, abundant. The reference, however, is to the manna, with which the people were supplied from day to day, and which seemed to be showered upon them in abundance. The word rendered “didst send” means properly to shake out, as if God shook the clouds or the heavens, and the abundant supplies for their needs were thus shaken out.
Whereby thou didst confirm thine inheritance, when it was weary - Thou didst strengthen thy people when they were exhausted, or were in danger of fainting. In other words, God sent a supply of food - manna, quails, etc. - when they were in the pathless wilderness, and when they were ready to perish.