LGPL-3.0 is a “library” variant of GPL-3.0. If you modify the LGPL-3.0 library itself, your modifications must be released under LGPL-3.0. If you just use the library — link to it, call its APIs — your own code can stay under any license, even proprietary.
LGPL-3.0 is a good fit for reusable libraries where you want modifications to the library itself to stay open, but you are fine with the library being called from closed-source code.
How to apply
Add a LICENSE or COPYING.LESSER file with the full LGPL-3.0 text alongside the GPL-3.0 text it incorporates by reference. Each source file should carry an SPDX header:
// SPDX-License-Identifier: LGPL-3.0-only
Full license text
GNU LESSER GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
This version of the GNU Lesser General Public License incorporates
the terms and conditions of version 3 of the GNU General Public License,
supplemented by the additional permissions listed below.
0. Additional Definitions.
1. Exception to Section 3 of the GNU GPL.
2. Conveying Modified Versions.
3. Object Code Incorporating Material from Library Header Files.
4. Combined Works.
5. Combined Libraries.
6. Revised Versions of the GNU Lesser General Public License.
… this text is abbreviated.
For the complete license text, see https://www.gnu.org/licenses/lgpl-3.0.html
Raw text also available at /license-texts/LGPL-3.0.txt — handy for curl.