This is a bit complicated as there are two different issues.
To the extent that part of the payment was used to repair actual damage to your property, this is not taxable.
To the extent that part of the payment was to purchase a portion of your property (or to purchase an easement) that reduces your cost basis and might be taxable (but probably not). Your adjusted cost basis is what you originally paid, plus the cost of permanent improvements you have made over the years. Your cost basis is used to determine your taxable capital gains when you sell.
Let's make up an extreme example. You bought the house 40 years ago for $100,000 and never made any improvements. Your cost basis is $100,000. Due to real estate price increases, the house and land are now worth $1 million, and the county paid $150,000 for the easement. This reduces your cost basis to zero, and the remaining $50,000 is taxable as a long term capital gain (because you sold an interest in the property that you owned for more than one year.)
In a less silly example, suppose you bought the home for $200,000, and the easement was $10,000. Your adjusted basis is reduced to $190,000. The payment is not taxable now, but because it reduced your basis, your taxable capital gains will be higher and you could owe more capital gains tax if and when you sell.
