Abigail is the first storm to be given a name by the Met Office who keep track of our weather.
The storm will hit Northern Ireland with strong winds on Thursday afternoon, and move towards the west coast of Scotland and northern England on Friday.
As if one storm wasn't enough, the UK will also be battered by ex-hurricane Kate, which is the end of a hurricane from the Atlantic Ocean. Kate will bring lots more rain for Scotland, Wales and northern parts of England.
Weather forecasters have told people to make sure they are prepared for strong winds, especially in Scotland. Several schools have already shut in the Western Isles in Scotland because of the bad weather.

An "in-depth investigation" will look into claims made by Veracruz governor Miguel Angel Yunes Linares on Monday, the Ministry of Health said.
He alleged fake medicine had been bought and used in state hospitals under his predecessor Javier Duarte.
Mr Duarte has been on the run from the authorities since October.
The former governor, who was elected in 2010,  has not been seen since a week after he stepped down amid allegations of corruption.
He has been charged with organised crime and money laundering, but there are calls for the Attorney General's office to file criminal charges relating to the latest accusations.
On Monday, Mr Yunes Linares told a press conference that an investigation into malfeasance and corruption under Mr Duarte had uncovered medical fraud.
`We have tests on a medication given to children, a paediatric chemotherapy that wasn't really a medication, it was an inert substance, practically distilled water,'' he said.
"This really seems to us a brutal crime, an attempt against the lives of the children. We're finishing our analysis and, at the appropriate time, we'll be filing legal complaints."
Mr Yunes Linares also alleged there had been inadequate tests for HIV detection and the existence of outdated medicines.
The allegations have shocked Mexico.
"It is absolutely inhuman, criminal," Senator Roberto Gil Zuart said, according to Mexican news site Quadratin.
Mexico's Secretary of Health JosÃ© Narro Robles has promised to act on "the persons or companies involved" if irregularities or responsibility is found, the ministry said in a statement on Wednesday.

The 76-year-old, who received the Â£25,000 prize for Squint (19) at Liverpool's Walker Art Gallery, was one of the shortlisted artists in 1991.
Simpson, who has also made the prize longlist on three other occasions, said finally winning was "very nice indeed".
Judge Ansel Krut said Squint (19) was "quite extraordinary", even though it was a "difficult painting to look at".
The work depicts a leper squint, which Simpson said were "holes made in the sides of medieval churches so the undesirables could look through to the service and somehow take part".
He said it was one of a series of paintings he has been working on, some of which were "much bigger".
The relatively small size of Squint (19) - which is about 7ft (2.1m) in height - was one of the reasons Simpson entered it into the competition, though he also admitted that it "seemed to be a good idea to send one that I was conversant with and was working with".
He said the prize money would be spent on "stretches, canvas and - particularly - good quality paints".
"I spend a lot of money on materials, so this money is going to go to a good cause."
Krut said Simpson's piece was "a little bit like a tone poem - when you spend some time with it, it gradually starts to build a picture".
"Technically, it's very subtle and his language is very minimal, very reduced, but when you enter into it, you get into this broad field of great sympathy, because of the subject matter.
"We couldn't have asked for a better painting."
Established in 1957, the biennial John Moores Painting Prize is one of Britain's oldest art awards.
Previous winners include David Hockney and Peter Doig. Sir Peter Blake, who is now the prize's patron, won the junior title in 1961.
Much of the UK will be hit by Storm Abigail on Thursday, bringing lots of rain and strong winds.
[NEXT_CONCEPT]
Mexican authorities are to investigate allegations children battling cancer were given "distilled water" instead of chemotherapy.
[NEXT_CONCEPT]
Michael Simpson has won the John Moores Painting Prize, 25 years after he first came close to taking the title.