All of your mother's assets, including the value of her home (if relevant, and commencing from 12 weeks after she moves into a nursing home) will be included in the calculations unless her home is also occupied by her husband/partner or by a close relative who is over 60 and/or incapacitated.
While those assets are greater than £23,250 the system assumes that she'll pay for the full costs of nursing home care.
Once her assets fall below that level, but remain above £14,250, the system assumes that whatever she's got above £14,250 will generate an income of £1 per week for each £250 of her assets and that such money can contribute towards her care. For example, if she's got £19,250 in assets, she's got £5000 (= 20 x £250) above the £14,250 threshold. Therefore she'll be required to pay £20 per week towards her care, with the local authority funding the rest of it.
Once her assets fall below £14,250 the local authority must pay for everything.
https://www.nidirect.gov.uk/articles/paying-your-residential-care-or-nursing-home-fees